Can you pursue another degree while in college?

No. Not possible. A four year accredited university has a plan of courses towards a degree. These courses are accepted by the accreditation organization. Students enrolled at each school must complete the requirements set by that school alone. Some four year schools accept transfer of some students from community colleges approved, not all. Community colleges were born as vocational schools and adopted the term "college" but they are not in the same league. I have no clue as to the purpose of this posting as most college students have enough of a work load that prevents them from doing anything else. Community colleges offer an Associate's Degree. While better than a high school diploma it is not by far and not comparable to a four year accredited Bachelor's degree.

That's a bad idea.

If you want a second subject, get a master's degree after you finish the undergraduate degree. Or, get a certificate in the second subject.

Yes you can. Best option is online courses. Now a days many universities provided online courses. This courses is time saving and helpful to career. http://www.adtuonline.edu.in/

I think it might be possible. Its best to talk to a adviser about it they know more than I do.